Profit and Loss Question 3 - CAT 2020
A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by percent so as to make an overall profit of 15%. Then
is nearest to:
Step-by-Step Explanation
Let the cost price of 1 kg of sugar be Rs. 100.
- Total Cost Price (CP) for 35 kg = 35 × 100 = Rs. 3500.
- Targeted overall profit = 15%, so the required total Selling Price (SP) is:
Targeted SP = 3500 × 1.15 = Rs. 4025
The initial marked price (MP) per kg is set for a 20% profit:
MP = Rs. 120/kg
- First Sale: 5 kg sold at MP → 5 × 120 = Rs. 600.
- Second Sale: 15 kg sold at a 10% discount on MP → 15 × 120 × 0.90 = 15 × 108 = Rs. 1620.
- Wastage: 3 kg of sugar is lost (generates Rs. 0).
Remaining quantity of sugar to sell:
Remaining Sugar = 35 − 5 − 15 − 3 = 12 kg
Current revenue accumulated:
Current SP = 600 + 1620 = Rs. 2220
Balance revenue needed to reach the target:
Balance Needed = 4025 − 2220 = Rs. 1805
New selling price required per kg for the remaining 12 kg:
New SP per kg = 1805 / 12 ≈ Rs. 150.42
The original marked price was Rs. 120. The percentage increase p required on this marked price is:
p = [(150.42 − 120)] / 120 × 100
= (30.42 / 120) × 100
≈ 25.35%
The nearest whole integer is 25.
Correct Option: C
💡 FundaMakers Tip:
When handling multi-stage commercial transactions where quantities break down or get wasted, assume a base value of Rs. 100. Maintain a simple running tally of Revenue Collected versus Target Revenue. This keeps the remaining required cash flow clear and prevents tracking errors.